Honestly, "I think he's lying" seems to me like it's skipping over it as well since it's the player's determination of how their PC feels rather than looking for any evidence that might have them rendering that judgment. So, no check necessary, I guess?
The player is in full control over how their character thinks, acts, and speaks - as 5e defines roleplaying. If they think he's lying, that's what they think. What a character thinks and what is true in the world can be different, however.
Now, is he lying? That's something that an Insight check might answer.